This study describes the identification of Drosophila yellow-f and yellow-f2 as dopachrome-conversion enzymes responsible for catalysing the conversion of dopachrome into 5,6-dihydroxyindole in the melanization pathway. Drosophila yellow -y gene and yellow -b, -c, -f and -f2 genes were expressed in an insect cell/baculovirus expression system and their corresponding recombinant proteins were sc...

Given two maps f1, f2 : M −→ N between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC(f1, f2) of pathcomponents of the coincidence space of maps f ′ 1 , f ′ 2 where f ′ i is homotopic to fi, i = 1, 2 ? Approaching this question via normal bordism theory we define a lower bound N(f1, f2) which gener...

The notation and terminology used here are introduced in the following papers: [13], [15], [1], [16], [2], [4], [10], [11], [17], [5], [14], [12], [3], [7], [6], [9], and [8]. For simplicity, we adopt the following convention: x, a, b, c denote real numbers, n denotes a natural number, Z denotes an open subset of R, and f , f1, f2 denote partial functions from R to R. Next we state a number of ...

Let n and r be positive integers. Suppose that a family F ⊂ 2[n] satisfies |F1 ∩ F2 ∩ F3| ≥ 2 for all F1, F2, F3 ∈ F . We prove that if w < 0.5018 then ∑ F∈F w |F |(1− w)n−|F | ≤ w2.

We investigate the complexity of the following computational problem: POLYNOMIAL ENTROPY APPROXIMATION (PEA): Given a low-degree polynomial mapping p : F → F, where F is a finite field, approximate the output entropy H(p(Un)), where Un is the uniform distribution on F and H may be any of several entropy measures. We show: • Approximating the Shannon entropy of degree 3 polynomials p : F2 → F2 o...

Let In = {0, 1}n, and Hn be the set of all functions from In to In. For f ∈ Hn, define the DES-like transformation associated with f by F2n,f (L, R) = (R ⊕ f(L), L), where L, R ∈ In. For f1, f2, . . . , fs ∈ Hn, define ψ(fs, . . . , f2, f1) = F2n,fs ◦ · · · ◦ F2n,f2 ◦ F2n,f1 . Our main result is that ψ(f, f j , f ) is not pseudorandom for any positive integers i, j, k, where f i denotes the i-f...

We obtain formulae and estimates for character sums of the type S(χ, f, pm) = ∑pm x=1 χ(f(x)), where p m is a prime power with m ≥ 2, χ is a multiplicative character (mod pm), and f = f1/f2 is a rational function over Z. In particular, if p is odd, d = deg(f1) + deg(f2) and d∗ = max(deg(f1), deg(f2)) then we obtain |S(χ, f, pm)| ≤ (d− 1)pm(1− 1 d∗ ) for any non constant f (mod p) and primitive ...

For a positive integer d⩾2, family F⊆([n]k) is said to be d-wise intersecting if |F1∩F2∩…∩Fd|⩾1 for all F1,F2,…,Fd∈F. A called maximal F∪{A} not any A∈([n]k)∖F. We provide refinement of O'Neill and Verstraëte's Theorem about the structure largest second non-trivial k-uniform families. also determine third fourth families k>d+1⩾4, fifth sixth 3-wise k⩾5, in asymptotic sense. Our proofs are appli...